System and method for correlating received signal over time and frequency

ABSTRACT

A system is provided for use with a frequency band including a transmission frequency and a received frequency. The transmission frequency includes a transmission signal having a transmitted unique word therein. The received frequency includes a received signal having a received unique word therein, wherein the received unique word had been received at a received time and at a received phase. The system includes a first sub-correlator, a second sub-correlator and a discrete Fourier transform device. The first sub-correlator can perform a first correlation of only a first portion of the received unique word with a corresponding first portion of the transmitted unique word over a plurality of instances of time and can output a first plurality of sub-correlation values. The second sub-correlator can perform a second correlation of only a second portion of the received unique word with a corresponding second portion of the transmitted unique word over the plurality of instances of time and can output a second plurality of sub-correlation values. The discrete Fourier transform device can perform a discrete Fourier transform over a plurality of frequencies within the frequency band on the first plurality of sub-correlation values and can perform a discrete Fourier transform over the plurality of frequencies within the frequency band on the second plurality of sub-correlation values. The first portion of the received unique word is different from the second portion of the received unique word.

BACKGROUND

In some communications systems, a goal is the detection of a signal withsome unknown parameters in noise. For example, in a burst-modetransmission, the start of the burst is often marked using somerecognizable signal, or “Unique Word” (UW). This signal will typicallyarrive at the receiver with unknown (to a greater or less extent)timing, as well as unknown phase and frequency. The signal will alsohave been subjected to various impairments, such as additive whiteGaussian noise (AWGN).

FIG. 1 illustrates a block diagram of a conventional communicationsystem 100.

Communication system 100 includes a transmitter 102 and a receiver 104.

Receiver 104 receives information from transmitter 102 via acommunication channel 106. Transmitter transmits a transmitted signal108. Impairments to the reception of transmitted signal 108 by receiver104 are generated by conditions denoted as impairment sources 110external to transmitter 102 and receiver 104. Non-limiting examples ofimpairments include atmospheric noise, solar noise, cosmic noise,thermal noise, white noise, Gaussian noise and Doppler effect.Impairment sources 110 generate and inject impairments as denoted by animpairment 112. Interference by impairments 112 to transmitted signal108 is modeled as additive as denoted by a noise addition element 114.Noise addition element 114 adds transmitted signal 108 and impairments112 to generate a noisy signal 116. Receiver 104 receives and processesnoisy signal 116. In order to receive and process noisy signal 116,receiver 104 performs processing steps, non-limiting examples of whichinclude filtering, mixing and correlation.

FIG. 2 illustrates an example communications protocol 200 that istransmitted by conventional transmitter 102 (FIG. 1).

Communications protocol 200 includes a plurality of frames with asampling denoted as a frame 204 and a frame 206.

Frame 204 and frame 206 are configured with respect to an x-axis 202with units of time and resolution of seconds.

Transmission of frame 204 initiates at a time 208 and terminates at atime 210. Transmission of frame 206 initiates at a time 212 andterminates at a time 214.

Frame 204 includes a unique word 216 and a payload 218. Unique wordprovides a mechanism for receiver 104 to synchronize with frame 204.Payload 218 includes data and information desired by transmitter 102 tobe received and processed by receiver 104. Transmission of unique word216 initiates at time 208 and terminates at a time 220. Transmission ofpayload 218 initiates at time 220 and terminates at time 210.

Unique word 216 includes a plurality of symbols with a sampling denotedas a symbol 222 and a symbol 224. Transmission of symbol 222 initiatesat time 208 and terminates at a time 226. Transmission of symbol 224initiates at a time 228 and terminates at time 220. Payload 218 includesa plurality of symbols with a sampling denoted as a symbol 230 and asymbol 232. Transmission of symbol 230 initiates at time 220 andterminates at a time 234. Transmission of symbol 232 initiates at a time236 and terminates at time 210.

Receiver 104 receives unique word 216 followed by payload 218. Receiver104 knows in advance the symbol structure of unique word 216 and seeksto find unique word 216 by performing a correlation operation. Once athreshold has been met for the correlation operation, receiver 104determines a starting time for the first symbol received of unique word216, as denoted by time 208. Once receiver has determined the startingtime for the initial symbol received, receiver 104 has also determinedthe initial time of reception for frame 204, as denoted by time 208.Receiver then uses the determination of time for initial reception offrame 204, as denoted by time 208, to synchronize and process thesymbols of payload 218.

FIG. 3 illustrates a graph 302, a graph 304 and a graph 306 forexplaining a conventional continuous correlation operation 300.

Conventional continuous correlation operation 300 may be described bythe following:

∫y(t−τ)x*(t)dt  (1)

For equation (1), x and y represent general complex-valued signals and τrepresents an estimate for the starting time of the received signal.

Graph 302 describes the characteristic of x or equation (1), graph 304describes the characteristic of y of equation (1) and graph 306describes the result of performing a correlation operation between x andy or graph 302 and graph 304.

Graph 302 includes an x-axis 308 with units of time in increments ofseconds and a y-axis 310 with units of height. A function 312 initiatesat a time 314 and terminates at a time 316. Function 312 has a height asdesignated by a height 318.

Graph 304 includes an x-axis 320 with units of time in increments ofseconds and a y-axis 322 with units of height. A function 324 initiatesat a time 326 and terminates at a time 328. Function 324 has a height asdesignated by a height 330.

Graph 306 includes an x-axis 332 with units of time in increments ofseconds and a y-axis 334 with units of height. A function 336 representsthe correlation of function 312 of graph 302 with function 324 of graph304 as described by equation (1). Function 336 initiates at a time 338and increases linearly to a point 340 at a time 342 with a maximum valueas denoted by a maximum value 344. Following this, function 336decreases linearly and terminates at a time 346 with a height of zero. Athreshold value as denoted by a threshold height 350 crosses function336 at a point 348 with x-axis 332 value as represented by a time 352and also at a point 354 with x-axis 332 value as represented by a time356.

For receiver 104, threshold height 350 represents a condition of apotential match between a received signal and an expected signal, asdenoted between time 352 and time 356, with point 340 representing anexact match between a received signal and an expected signal. Receiver104 uses correlation to determine when a received signal has matched anexpected signal and then uses the timing information to decode andprocess received information from a received signal.

In the case of AWGN in particular, it is well known that a signal can beoptimally detected by computing the correlation between the knowntransmitted signal and the received signal, and finding the value oftime τ which maximizes the magnitude of the correlation as given by thefollowing equation:

$\begin{matrix}{\hat{\tau} = {\underset{\tau}{\arg \max}{{\int{{y( {t - \tau} )}{x^{*}(t)}{t}}}}^{2}}} & (2)\end{matrix}$

Where x and y in equation (2) are in general complex-valued signals andτ is the estimate of the starting time of the received signal. Thevariable x describes a sequence of predetermined symbols of a uniqueword and variable y represents a received sequence of symbols.

Typically digital sampled signals are being processed, and thecorrelation is replaced by the summation as shown below:

$\begin{matrix}{\hat{\tau} = {{{nT}\mspace{14mu} {where}\mspace{14mu} n} = {\underset{n}{\arg \; \max}{{\sum\limits_{i = 1}^{M}{y_{i - n}x_{i}^{*}}}}^{2}}}} & (3)\end{matrix}$

For equation (3), T represents a sampling period.

In addition to unknown timing and phase, a received signal may also haveunknown frequency offset, within a range. The frequency offset willcause a phase shift over the length of the received signal. This willcause the correlation to be reduced or negatively affected. Thereduction in correlation may be described as:

$\begin{matrix}{{\frac{1}{T}{\int_{{- T}/2}^{T/2}{{\cos( {2\pi \; f\; t}\  )}{t}}}} = \frac{\sin ( {\pi \; {fT}} )}{\pi \; {fT}}} & (4)\end{matrix}$

For equation (4), f represents a frequency offset and T represents thelength of time for the correlation. As may be observed, if the frequencyoffset relative to the correlation length becomes large, the peak valueof the correlation may be reduced and as a result of the reduction incorrelation, the detection performance may be degraded.

Three solutions to problems applying correlation to received signalswith a frequency offset have been applied. One solution is nearlyoptimal, but highly complex. The other two solutions are lesscomplicated, but experience suboptimal performance.

The first solution discussed may be referred to as a “brute force”approach where a search is performed over time and frequency. Instead ofperforming a single correlation as shown above, a bank of correlatorsmay be used. The input to each correlator may be referred to as a signaly which has been frequency shifted by some increment. The maximizationis taken over all the correlation magnitude values. In the limit ofcontinuous time and frequency, this may be described as equivalent to:

$\begin{matrix}{\hat{\tau} = {\underset{f,\tau}{\arg \; \max}{{\int{{y( {t - \tau} )}^{j\; 2\pi \; f\; t}{x^{*}(t)}{t}}}}^{2}}} & (5)\end{matrix}$

Typically, a discrete time and frequency approximation to (5) may beused as shown below:

$\begin{matrix}{\hat{\tau} = {{{nT}\mspace{14mu} {where}\mspace{14mu} n} = {\underset{n,m}{\arg \; \max}{{\sum\limits_{i = 1}^{M}{y_{i - n}^{j\; 2{\pi }\; m\; F}x_{i}^{*}}}}^{2}}}} & (6)\end{matrix}$

For equation (6), mF represents some multiple of frequency samplinginterval F. While this approach may perform well, it has replaced asingle correlation with a bank of correlations, one for each discretefrequency.

FIG. 4 illustrates a block diagram of a conventional brute forcereceiver portion 400.

Brute force receiver portion 400 includes a plurality of correlatorswith a sampling denoted as a correlator 402, a correlator 404 and acorrelator 406, a plurality of magnitude portions with a samplingdenoted as a magnitude portion 408, a magnitude portion 410 and amagnitude portion 412 and a maximum calculation portion 414.

Correlator 402, correlator 404 and correlator 406 receive a signal via acommunication channel 416 from external to brute force receiver portion400. Furthermore, correlator 402 receives a signal 418 representing adiscrete frequency offset denoted as 1F. Correlator 404 receives asignal 426 representing a discrete frequency offset denoted as 2F.Correlator 406 receives a signal 432 representing a discrete frequencyoffset denoted as mF, where m represents a value of maximum incrementfor frequency offset F.

Magnitude portion 408 receives a signal 420 from correlator 402.Magnitude portion 410 receives a signal 428 from correlator 404.Magnitude portion 412 receives a signal 434 from correlator 406 andoutput a signal 424.

Correlator 402, correlator 404 and correlator 406 receives a signal viacommunication channel 416 for processing via a correlation algorithm.Magnitude portion 408, magnitude portion 410 and magnitude portion 412receives correlated signals from correlator 402, correlator 404 andcorrelator 406, respectively, for performing a magnitude calculation.Finally, maximum calculation portion 414 receives a signal which has hada correlation calculation and magnitude calculation performed via asignal 422, a signal 430 and a signal 436. Maximum calculation portion414 determines which received signal has the largest magnitude. Thesignal with the largest magnitude and a value larger than a certainthreshold may then be processed for timing information for retrievingreceived data information as received via communication channel 416.

While application of the brute force correlation method may performwell, it has replaced a single correlation with a bank of correlations,one for each discrete frequency. In other words, a correlator may searchfor the entire Unique Word over all frequencies and all times.Application of the brute force correlation method is very expensive toimplement, especially in environments where size, weight, powerconsumption and power dissipation are considered a premium, such as insatellite or military applications.

A second approach for processing a correlation of a received signal isto break the correlation into shorter correlation intervals, and thencombine the outputs of these subintervals non-coherently as shown below:

$\begin{matrix}{{\hat{\tau} = {nT}}{{{where}\mspace{14mu} n} = {\underset{n}{\arg \; \max}\{ {{{\sum\limits_{i = 1}^{L}{y_{i - n}x_{i}^{*}}}}^{2} + {{\sum\limits_{i = L}^{2L}{y_{i - n}x_{i}^{*}}}}^{2} + \ldots}\mspace{14mu} \}}}} & (7)\end{matrix}$

FIG. 5 illustrates a block diagram of a conventional non-coherentreceiver portion 500.

Conventional non-coherent receiver portion 500 includes a unique wordportion 504, a plurality of sub-correlators with a sampling denoted as asub-correlator 506, a sub-correlator 508 and a sub-correlator 510, aplurality of delay portions with a sampling denoted as a delay portion512, a delay portion 514 and a delay portion 516, a plurality ofmagnitude portions with a sampling denoted as a magnitude portion 518, amagnitude portion 520 and a magnitude portion 522 and a summationportion 524.

Sub-correlator 506 receives a signal from a communication channel 526and receives a signal 552 from unique word portion 504. Magnitudeportion 518 receives a signal 528 from sub-correlator 506. Delay portion512 receives a signal from communication channel 526. Sub-correlator 508receives a signal 532 from delay portion 512 and a signal 550 fromunique word portion 504. Magnitude portion 520 receives a signal 534from sub-correlator 508. Delay portion 514 receives signal 532 fromdelay portion 512. Delay portion 516 receives a signal 538 generatedfrom a plurality of delay portions. Sub-correlator 510 receives a signalfrom delay portion 516 via a signal 540 and from unique word portion 504via a signal 548. Magnitude portion 522 receives a signal 542 fromsub-correlator 510. Summation portion 524 receives a signal frommagnitude portion 518 via a signal 530, from magnitude portion 520 via asignal 536, from magnitude portion 522 via a signal 544 and from aplurality of other magnitude portions not shown.

Unique word portion 504 includes a plurality of unique word sub-portionswith a sampling denoted as a unique word sub-portion 554, a unique wordsub-portion 556 and a unique word sub-portion 558. Unique wordsub-portion 554 includes a plurality of symbols with a sampling denotedas a symbol 560 and a symbol 562. Unique word sub-portion 556 includes aplurality of symbols with a sampling denoted as a symbol 564 and asymbol 566. Unique word sub-portion 558 includes a plurality of symbolswith a sampling denoted as a symbol 568 and a symbol 570.

Unique word portion 504 is configured with respect to an x-axis 502 withunits of time and resolution of seconds. Unique word portion 504represents a predetermined sequence of symbols to be received in orderto perform synchronization, decoding and processing. Symbols of uniqueword sub-portions correspond to a relation with respect to x-axis 502for order of transmission and arrival. For example symbol 560 of uniqueword sub-portion 554 may be considered the first symbol to be receivedfor a frame of data provided from a transmitter, whereas, symbol 570 ofunique word sub-portion 558 may be considered the last received symbolfor the unique word portion of a frame with payload symbols to follow.

Sub-correlator 506 receives a signal via communication channel 526 andperforms a correlation of the received signal with the symbols receivedfrom unique word sub-portion 558. Sub-correlator 508 my receives adelayed signal from communication channel 526 via delay portion 512 andperforms a correlation of the delayed received signal with the symbolsof unique word sub-portion 556. Sub-correlator 510 receives a multiplieddelayed signal from communication channel 526 and performs a correlationof the delayed received signal with the symbols of unique wordsub-portion 554.

Magnitude portion 518 receives a signal from sub-correlator 506 andperforms a magnitude calculation. Magnitude portion 520 receives asignal from sub-correlator 508 and performs a magnitude calculation.Magnitude portion 522 receives a signal from sub-correlator 510 andperforms a magnitude calculation. Summation portion 524 receives a setof magnitude calculations from magnitude portion 518, magnitude portion520, magnitude portion 522 and a plurality of other magnitude portionsnot shown and performs a summation calculation. The summationcalculation may be compared to threshold in order to determine if aunique word has been received as denoted by the configuration of uniqueword portion 504. Once the threshold has been achieved, the signalreceived via communication channel 526 may then be processed for timinginformation for retrieving received data information as received viacommunication channel 526.

With the conventional non-coherent receiver approach, a singlecorrelator may be required, however the drawback is that the performanceof the correlator in noisy conditions is degraded due to thenon-coherent summation performed for the sub-correlations.

A third approach for processing a correlation of a received signal is toapply differential detection. For differential detection, a differentialdetection operation is performed on the received sequence of symbols toform a new sequence described as:

y′ _(i) =y _(i) y* _(i-1).  (8)

The new sequence is then correlated with an expected differentialsequence described as:

x′ _(i) =x _(i) x* _(i-1)  (9)

FIG. 6 illustrates a block diagram of a conventional differentialdetection receiver portion 600.

Conventional differential detection receiver portion 600 includes adelay 602, a differential portion 604, a unique word portion 606, adelay 608, a differential portion 610 and a correlator 612.

Delay 602 receives a signal via a communication channel 614.Differential portion 604 receives a signal from communication channel614 and a delayed version of the signal from delay 602 via a signal 616.Delay 608 receives a signal 620 from unique word portion 606.Differential portion 610 receives a signal 622 from unique word portion606 and a delayed or shifted version of unique word from delay 608 via asignal 624. Correlator portion 612 receives a received differentialsignal from differential portion 604 via a signal 618 and an expecteddifferential signal from differential portion 610 via a signal 626.Correlator 612 provides a signal external to conventional differentialdetection receiver portion 600 via signal 618.

Unique word portion 606 provides storage for an expected unique word tobe received via communication channel 614. Delay 608 provides a delayedor shifted version of unique word portion 606. Differential portion 610performs a differential operation on the unique word stored in uniqueword portion 606 and a delayed or shifted version of the unique wordstored in unique word portion 606. Delay 602 provides a delayed versionof the signal received via communication channel 614. Differentialportion 604 performs a differential operation on the signal received viacommunication channel 614 and the delayed version of the signal receivedfrom delay 602. Correlator 612 performs a correlation operation on thedifferential operation performed on the unique word stored in uniqueword portion 606 and the differential Operation performed on the signalreceived via communication channel 614 and the delayed version of thesignal received via communication channel 614.

Signal 628 generated by correlator 612 is compared to a threshold inorder to determine if a unique word has been received as denoted by theconfiguration of unique word portion 606. Once the threshold has beenachieved, the signal received via communication channel 614 is thenprocessed for timing information for retrieving received datainformation as received via communication channel 614.

An advantage of the conventional differential detection approach is thatit is inherently insensitive to issues related to frequency offsets.However, the drawback to this approach is it can suffer a significantperformance loss due to the differential detection step. Furthermore,the losses due to differential detection increase as the signal-to-noiseratio decreases.

What is needed is a system and method for optimally or near optimallydetecting and decoding information embedded in a signal withoutnecessitating a large number of correlator banks for implementation.

BRIEF SUMMARY

The present invention provides a system and method for nearly optimalperformance for searching a signal over both time and frequency, and fordecoding and processing information embedded within the received signal.

In accordance with an aspect of the present invention, a system andmethod is provided for use with a frequency band including atransmission frequency and a received frequency. The transmissionfrequency includes a transmission signal having a transmitted uniqueword therein. The received frequency includes a received signal having areceived unique word therein, wherein the received unique word had beenreceived at a received time and at a received phase. The system includesa first sub-correlator, a second sub-correlator and a discrete Fouriertransform device. The first sub-correlator can perform a firstcorrelation of only a first portion of the received unique word with acorresponding first portion of the transmitted unique word over aplurality of instances of time and can output a first plurality ofsub-correlation values. The second sub-correlator can perform a secondcorrelation of only a second portion of the received unique word with acorresponding second portion of the transmitted unique word over theplurality of instances of time and can output a second plurality ofsub-correlation values. The discrete Fourier transform device canperform a discrete Fourier transform over a plurality of frequencieswithin the frequency hand on the first plurality of sub-correlationvalues and can perform a discrete Fourier transform over the pluralityof frequencies within the frequency band on the second plurality ofsub-correlation values. The first portion of the received unique word isdifferent from the second portion of the received unique word

Additional advantages and novel features of the invention are set forthin part in the description which follows, and in part will becomeapparent to those skilled in the art upon examination of the followingor may be learned by practice of the invention. The advantages of theinvention may be realized and attained by means of the instrumentalitiesand combinations particularly pointed out in the appended claims.

BRIEF SUMMARY OF THE DRAWINGS

The accompanying drawings, which are incorporated in and form a part ofthe specification, illustrate an exemplary embodiment of the presentinvention and, together with the description, serve to explain theprinciples of the invention. In the drawings:

FIG. 1 illustrates a block diagram of a conventional communicationsystem;

FIG. 2 illustrates a conventional transmission of a communicationsprotocol by a transmitter as shown in FIG. 1;

FIG. 3 illustrates a conventional continuous correlation operation;

FIG. 4 illustrates a block diagram of a conventional brute forcereceiver portion;

FIG. 5 illustrates a block diagram of a conventional non-coherentreceiver portion;

FIG. 6 illustrates a block diagram of a conventional differentialdetection receiver portion;

FIG. 7 illustrates a block diagram of an example communication receiverportion, in accordance with an aspect of the present invention;

FIG. 8 illustrates a detailed version of an example data recoveryportion as shown in FIG. 7, in accordance with an aspect of the presentinvention;

FIG. 9 illustrates a detailed version of an example sub-correlatorportion as shown in FIG. 8, in accordance with an aspect of the presentinvention;

FIG. 10 illustrates a detailed version of an example digital Fouriertransform DFT portion as shown in FIG. 8, in accordance with an aspectof the present invention;

FIG. 11 illustrates a detailed version of an example phase-shift portionas shown in FIG. 10, in accordance with an aspect of the presentinvention;

FIG. 12 illustrates a detailed version of an example magnitude portionas shown in FIG. 8, in accordance with an aspect of the presentinvention;

FIG. 13 illustrates a detailed version of an example data processor asshown in FIG. 8, in accordance with an aspect of the present invention;

FIG. 14 illustrates an example matrix of magnitude information ascalculated by a data recovery portion as shown in FIGS. 7-8, inaccordance with an aspect of the present invention; and

FIGS. 15A-B illustrate an example method for operation of a dataprocessor as shown in FIG. 8 and FIG. 13, in accordance with an aspectof the present invention.

DETAILED DESCRIPTION

Generally a demodulator receives a waveform and outputs either harddecisions, i.e., binary 1 and binary 0, or outputs soft decisions,values determined to be either a binary 1 and binary 0. In particular, aburst-mode demodulator includes two functions: first, it estimatesparameters needed to decode a signal, e.g., time of the burst, frequencyof the burst, phase, etc.; and then 2) using the estimates, there is ademodulation process, e.g, similar to a continuous mode demodulation.Aspects of the present invention are drawn to the first function of aburst-mode demodulator, i.e., estimating parameters of the burst.

An aspect of the present invention provides nearly optimal performancefor searching a signal over both time and frequency. A correlationoperation may be performed between the received signal and apredetermined unique word. In the prior art brute force method discussedabove, an entire received unique word is correlated over a plurality oftime instances and over a plurality of frequencies. On the contrary, inaccordance with the present invention, the unique word is divided intosegments. Then, each segment is correlated over the plurality of timeinstances as a plurality of sub-correlations. The plurality ofsub-correlations is then correlated over the plurality of frequencies byway of a discrete Fourier transform (DFT). Consequently, the entireunique word is only correlated once over the plurality of time instancesand over the plurality of frequencies. Furthermore, the result of thephase shift and DFT performed for the sub-correlations may be considereda matrix of complex-values organized by time and frequency.

In other embodiments of the present invention, a method and system willbe described for performing a magnitude calculation for the resultsfollowing the performance of the DFT as described for the firstembodiment and for determining time and frequency offset to provide fordecoding information embedded in a received signal.

The matrix of real-valued magnitude information organized by time andfrequency may be stored for processing. The stored information may beretrieved and processed. Non-limiting example of processing performedmay include threshold detection and matrix operations. For determinationof a matrix element with a magnitude value greater than a threshold, atime and frequency offset may be ascertained.

Further processing may include examining neighboring values of theelement of the matrix with the maximum value for purposes of furtherrefining the time and frequency offset. For a determination ofsignificant neighboring values to the maximum value, an interpolationmay be performed for ascertaining a more accurate representation for thetime and frequency offset.

The resulting time and frequency offset information may be used fordecoding the embedded information located within the received signal.The decoded information may be delivered for a use of some purpose.

Initial discussion will focus on explaining the time element of thepresent invention. The output of the correlator at time j may bedescribed as:

$\begin{matrix}{c_{j} = {\sum\limits_{n}{y_{n + j}x_{n}^{*}}}} & (10)\end{matrix}$

Where x and y in equation (10) are generally complex-valued. Thevariable x may describe a sequence of predetermined symbols of a uniqueword and variable y may represent a received sequence of symbols.Equation (10) may describe the discrete correlation of y and x asdenoted by the summation of the sequence of y multiplied by the sequenceof x.

The discussion for frequency will now be considered as described by:

$\begin{matrix}{c_{j,k} = {\sum\limits_{n}{y_{n + j}x_{n}^{*}^{{- {2\pi}}\; {nkF}}}}} & (11)\end{matrix}$

For equation (11), F may describe a frequency increment, j may representa time index and k may represent a frequency index.

The summation calculation as performed by equation (11) may be broken upinto summations of smaller intervals as described by:

$\begin{matrix}{c_{j,k,l} = {\sum\limits_{n = {{lL} - 1}}^{{{({l + 1})}L} - 1}{y_{n + j}x_{n}^{*}^{{- 2}\pi \; {nkF}}}}} & (12)\end{matrix}$

For equation (12), l may represent an index over the subintervals.

The complete correlation for each time and frequency may be described asthe summation over all of the smaller intervals as described by:

$\begin{matrix}{c_{j,k} = {\sum\limits_{l}c_{j,k,l}}} & (13)\end{matrix}$

The substitution of equation (12) into equation (13) may be describedas:

$\begin{matrix}{c_{j,k} = {\sum\limits_{l}{\sum\limits_{n = {{lL} - 1}}^{{{({l + 1})}L} - 1}{y_{n + j}x_{n}^{*}^{{- }\; 2\pi \; {nkF}}}}}} & (14)\end{matrix}$

For equation (14), l may operate as an index over the subintervals.

The length of each subinterval for equation (14), as denoted by L, maybe chosen small enough such that the change in phase factor e^(−i2πnkF)over the interval may be considered as small. Furthermore, since thecontribution of the phase factor is very small for small subintervals,the phase factor may be removed from the inner summation to the outersummation as described by:

$\begin{matrix}{c_{j,k}\bullet {\sum\limits_{l}{^{{- {2\pi}}\; {klLF}}{\sum\limits_{n = {{lL} - 1}}^{{{({l + 1})}L} - 1}{y_{n + j}x_{n}^{*}}}}}} & (15)\end{matrix}$

Taking into account the change in phase between the subintervals may beconsidered as 2πkLF, equation (15) may be further simplified asdescribed by:

$\begin{matrix}{c_{j,k} = {\sum\limits_{l}{^{{- {2}}\; \pi \; {klLF}}c_{j,0,l}}}} & (16)\end{matrix}$

The length of the subcorrelation, as denoted by L, may be chosen smallenough such that the loss as described by equation (4) may be consideredacceptably small. This approach may produce a similar result asdescribed previously with respect to the brute force approach, albeitwith a small loss as described by equation (4). Furthermore, the resultof this approach may operate using a single correlator instead of a bankof correlators as used for the brute force approach.

Equation (16) has the form of a discrete Fourier transform (DFT). Thus,a DFT may be performed for the results generated from performing thesubinterval correlations.

In summary, the correlation sequence x and input sequence y are dividedinto l segments of length L. The correlation calculation for thesegments may be considered a vector of length M (i.e. r_(xy)(j), j=0 . .. M−1). The DFT may be applied over the l segments for each time indexj. The resulting output of the DFT may be considered a 2-dimensionalcomplex-valued matrix over time and frequency. For signals with unknownphase, a magnitude calculation may be performed for the output of theDFT, resulting in a 2-dimensional matrix of real-valued magnitudes overtime and frequency. The resulting 2-dimensional matrix may be processeddependant upon the application. For example, to find the highestcorrelation magnitude over time and frequency, the 2-dimensional matrixmay be searched for the highest value of magnitude.

A more detailed discussion for an exemplary embodiment of the presentinvention will now be described with respect to FIGS. 7-15.

FIG. 7 illustrates a block diagram of an example communication receiverportion 700, in accordance with an aspect of the present invention.

Communication receiver portion 700 includes a filter portion 702, aparameter estimator 704 and a demodulator portion 706. Each of theelements of communication receiver portion 700 are illustrated asindividual devices, however, in some embodiments of the presentinvention at least two of filter portion 702, parameter estimator 704and demodulator portion 706 may be combined as a unitary device.

Filter portion 702 may receive a communication signal via acommunication channel 708. Parameter estimator 704 may receiveinformation from filter portion 702 via a signal 710. Demodulatorportion 706 may receive information from parameter estimator 704 via asignal 712.

Filter portion 702 may receive a communication signal via communicationchannel 708 and perform a filtering function or functions on thereceived communication signal. Non-limiting examples of filtering whichmay be performed include band pass, high pass and low pass.

Parameter estimator 704 may receive the filtered signal from filterportion 702 and perform a demodulation function or functions.Non-limiting examples of demodulation which may be performed includeAmplitude, Frequency and Phase-shift Demodulation.

Demodulator portion 706 may receive the demodulated signal fromparameter estimator 704, perform processing for data recovery andreceive recovered data and information via a signal 714. Non-limitingexamples of processes which may be applied include mixing, correlating,delaying, matching, multiplying, performing magnitude calculations,phase shifting, performing summation calculations, performing matrixoperations, performing DFT calculations, performing complex conjugatecalculations and performing interpolation calculations.

Communication receiver portion 700 may receive a communication signalvia communication channel 708 and process the received signal such thatthe transmitted signal may be recovered and transmitted via signal 714.

FIG. 8 illustrates a detailed version of example parameter estimator 704and demodulator portion 706 (FIG. 7), in accordance with an aspect ofthe present invention.

Parameter estimator 704 includes a unique word portion 804, plurality ofcorrelators with a sampling denoted as a sub-correlator portion 806, asub-correlator portion 808 and a sub-correlator portion 810, a pluralityof delay portions with a sampling denoted as a delay portion 812, adelay portion 814 and a delay portion 816, a DFT portion 818, aplurality of magnitude portions, with a sampling denoted as a magnitudeportion 820, a magnitude portion 822 and a magnitude portion 824 and asignal parameter estimator 826. Each of the elements of parameterestimator 704 are illustrated as individual devices, however, in someembodiments of the present invention at least two of unique word portion804, plurality of correlators with a sampling denoted as sub-correlatorportion 806, sub-correlator portion 808 and sub-correlator portion 810,plurality of delay portions with a sampling denoted as delay portion812, delay portion 814 and delay portion 816, DFT portion 818, pluralityof magnitude portions, with a sampling denoted as magnitude portion 820,magnitude portion 822 and magnitude portion 824 and signal parameterestimator 826 may be combined as a unitary device.

Sub-correlator portion 806 may receive information via a signal 828generated external to parameter estimator 704 and receive a signal 860from unique word portion 804. Sub-correlator portion 806 may thencorrelate signal 828 with signal 860 to generate signal 836. Delayportion 812 may receive information via signal 828. Sub-correlatorportion 808 may receive a signal 830 from delay portion 812 and a signal858 from unique word portion 804. Sub-correlator portion 808 may thencorrelate signal 830 with signal 858 to generate signal 838. Delayportion 814 may receive signal 830 from delay portion 812 and provide anoutput signal 831 to other delay portions (not shown). Delay portion 816may receive a signal 832 from other delay portions (not shown).Sub-correlator portion 810 may receive a signal 834 from delay portion816 and a signal 856 from unique word portion 804. Sub-correlatorportion 810 may then correlate signal 834 with signal 856 to generatesignal 840. DFT portion 818 may receive a signal 836 from sub-correlatorportion 806, a signal 838 from sub-correlator portion 808, a signal 840from sub-correlator portion 810 and a plurality of signals from othersub-correlator portions (not shown). Magnitude portion 820 may receive asignal 842 from DFT portion 818. Magnitude portion 822 may receive asignal 844 from DFT portion 818. Magnitude portion 824 may receive asignal 846 from DFT portion 818. A plurality of other magnitude portions(not shown) may receive signals from DFT portion 818. Signal parameterestimator 826 may receive a signal 848 from magnitude portion 820, asignal 850 from magnitude portion 822, a signal 852 from magnitudeportion 824 and a plurality of signals from other magnitude portions(not shown). Signal parameter estimator 826 may provide signal 712 forexternal connection from parameter estimator 704.

Unique word portion 804 includes a plurality of unique word sub-portionswith a sampling denoted as a unique word sub-portion 862, a unique wordsub-portion 864 and a unique word sub-portion 866. Unique wordsub-portion 862 includes a plurality of symbols with a sampling denotedas a symbol 868 and a symbol 870. Unique word sub-portion 864 includes aplurality of symbols with a sampling denoted as a symbol 872 and asymbol 874. Unique word sub-portion 866 includes a plurality of symbolswith a sampling denoted as a symbol 876 and a symbol 878.

Unique word portion 804 may be configured with respect to an x-axis 802with units of time and resolution of seconds. Unique word portion 804may represent a predetermined sequence of symbols to be received inorder to perform synchronization, decoding and processing. Symbols ofunique word sub-portions correspond to a relation with respect to x-axis502 for order of transmission and arrival. For example symbol 868 ofunique word sub-portion 862 may be considered the first symbol to bereceived for a frame of data provided from a transmitter, whereas,symbol 878 of unique word sub-portion 866 may be considered the lastreceived symbol for the unique word portion of a frame with a payload ofsymbols to follow.

Sub-correlator portion 806 may receive signal 828 and perform acorrelation of the received signal with the symbols received from uniqueword sub-portion 866. Sub-correlator portion 808 may receive a delayedsignal 828 via delay portion 812 and perform a correlation of thedelayed signal with the symbols provided by unique word sub-portion 864.Sub-correlator portion 810 may receive a multiply delayed signal ofsignal 828 via a plurality of delays and perform a correlation of thedelayed received signal with the symbols provided by unique wordsub-portion 862. A plurality of other correlators (not shown) mayreceive a plurality of delayed signals (not shown) of signal 828 via aplurality of delays (not shown) and perform a correlation of the delayedreceived signals with the symbols provided by unique word sub-portions(not shown).

DFT portion 818 may received the correlated signals from sub-correlatorportion 806, sub-correlator portion 808 and sub-correlator portion 810and from a plurality of other correlators (not shown) and perform a DFToperation on the received signals.

Magnitude portion 820, magnitude portion 822, magnitude portion 824 anda plurality of other magnitude portions (not shown) may receive signalsfrom DFT portion 818 and perform a magnitude calculation on the receivedsignals.

Signal parameter estimator 826 may receive the signals from magnitudeportion 820, magnitude portion 822, magnitude portion 824 and aplurality of other magnitude portions (not shown) and perform processingfunctions. Non-limiting examples of the processing functions performedby signal parameter estimator 826 include threshold calculations,threshold comparisons, time related calculations, frequency relatedcalculations, interpolation calculations and decoding operations. Signal712 output from signal parameter estimator 826 may include estimates ofparameters needed to demodulate the received signal. Non-limitingexamples of parameters includes signal timing and frequency. Demodulator706 may then use the estimates within signal 712 to demodulate uniqueword 804 and the payload to output signal 714.

Demodulator portion 706 may receive a signal containing information andperform correlations of sub-portions of the received signal withsub-portions of a unique word. A DFT portion may receive the results ofthe sub-correlation operations and perform a DFT operation. Magnitudeportions may receive the results of the DFT operation and performmagnitude calculations. A data processor portion may receive themagnitude calculations and perform processing of the magnitudeinformation to recover data information from the received signal.

FIG. 9 illustrates a detailed version of example sub-correlator portion806 (FIG. 8), in accordance with an aspect of the present invention.

Sub-correlator portion 808 (FIG. 8), sub-correlator portion 810 (FIG. 8)and a plurality of sub-correlator portions (not shown) may also bedescribed by the illustration of FIG. 9.

Sub-correlator portion 806 includes a multiplier portion 902 and asummation portion 904. Each of the elements of sub-correlator portion806 are illustrated as individual devices, however, in some embodimentsof the present invention at least two of multiplier portion 902 andsummation portion 904 may be combined as a unitary device.

Multiplier portion 902 may receive a data signal 906 and a unique wordsignal 908 generated external to sub-correlator portion 810. Summationportion 904 may receive a signal 910 from multiplier portion 902 andprovide a signal 912 for external connection from sub-correlator portion806.

Multiplier portion 902 may perform a multiplication operation ofinformation received from data signal 906 with information received fromunique word signal 908. Summation portion 904 may receive themultiplication information generated by multiplier portion 902 andperform a summation operation.

Sub-correlator portion 806 may receive data information and unique wordinformation and perform a multiplication of the received information.Furthermore, sub-correlator portion 806 may perform a summationcalculation for the information generated from the multiplicationoperation.

FIG. 10 illustrates a detailed version of example DFT portion 818 (FIG.8), in accordance with an aspect of the present invention.

DFT portion 818 includes a plurality of phase-shift portions, with asampling denoted as a phase-shift portion 1002, a phase-shift portion1004, a phase-shift portion 1006, a plurality of phase-shiftcoefficients, with a sampling denoted as a phase-shift coefficient 1008,a phase-shift coefficient 1010 and a phase-shift coefficient 1012. Eachof the elements of DFT portion 818 are illustrated as individualdevices, however, in some embodiments of the present invention at leasttwo of phase-shift portion 1002, phase-shift portion 1004, phase-shiftportion 1006, a plurality of phase-shift coefficients, with a samplingdenoted as phase-shift coefficient 1008, phase-shift coefficient 1010and phase-shift coefficient 1012 may be combined as a unitary device.

Phase-shift portion 1002 may receive a signal 1014 generated fromexternal to DFT portion 818, receive a phase-shift coefficient fromphase-shift coefficient 1008 via a signal 1016 and provide a signal 1018for connection external to DFT portion 818. Phase-shift portion 1002 mayreceive a signal 1020 from generated external to OFT portion 818,receive a phase-shift coefficient from phase-shift coefficient 1010 viaa signal 1022 and provide a signal 1024 for connection external to DFTportion 818. Phase-shift portion 1006 may receive a signal 1026generated from external to DFT portion 818, receive a phase-shiftcoefficient from phase-shift coefficient 1012 via a signal 1028 andprovide a signal 1030 for connection external to DFT portion 818. Aplurality of phase-shift portions (not shown) may receive a plurality ofsignals generated from external to DFT portion 818 (not shown), mayreceive a plurality of phase-shift coefficients from a plurality ofphase-shift coefficient portions (now shown) via a plurality of signals(now shown) and provide a plurality of signals (not shown) forconnection external to OFT portion 818.

Phase-shift portion 1002, phase-shift portion 1004, phase-shift portion1006 and a plurality of phase-shift portions (not shown) may perform aphase shift as denoted by a received phase-shift coefficient, perform aDFT for a received signal and deliver the results of the combinedphase-shift and DFT operation external to OFT portion 818.

DFT portion 818 may receive a plurality of signals deliveringsub-correlations performed between sub-signals and unique wordsub-portions. Furthermore, a plurality of differing phase shiftoperations and DFT operations may be applied to the receivedsub-correlations for generating a plurality of signals 842, 844 and 846.

FIG. 11 illustrates a detailed version of example phase-shift portion1002 (FIG. 10), in accordance with an aspect of the present invention.

Phase-shift portion 1004 (FIG. 10), phase-shift portion 1006 (FIG. 10)and a plurality of phase-shift portions (not shown) may also bedescribed by the illustration of FIG. 11.

Phase-shift portion 1002 includes a coefficient select portion 1102, acoefficients portion 1104, a multiplier portion 1106 and a summationportion 1108. Each of the elements of phase-shift portion 1002 areillustrated as individual devices, however, in some embodiments of thepresent invention at least two of coefficient select portion 1102,coefficients portion 1104, multiplier portion 1106 and summation portion1108 may be combined as a unitary device.

Coefficient select portion 1102 may receive a signal 1110 generatedexternal to phase-shift portion 1002 and may receive a signal 1112 fromcoefficients portion 1104. Multiplier portion 1106 may receive a signal1114 generated external to phase-shift portion 1002 and a signal 1116from coefficient select portion 1102. Summation portion 1108 may receivea signal 1118 from multiplier portion 1106 and generate a signal 1120for delivery external to phase-shift portion 1002.

Coefficient select portion 1102 may receive a coefficient indicationfrom external to phase-shift portion 1002 for selecting a group ofcoefficients from coefficients portion 1104 for delivery to multiplierportion 1106. Multiplier portion 1106 may receive the selected group ofcoefficients from coefficient select portion 1102 and receive asub-correlation calculation generated external to phase-shift portion1002 and perform a multiplication of the received signal with theselected group of coefficients. Summation portion 1108 may receive themultiplication calculation performed by multiplier portion 1106 andprovide the summation result external to phase-shift portion 1002.

FIG. 12 illustrates a detailed version of example magnitude portion 820(FIG. 8), in accordance with an aspect of the present invention.

Magnitude portion 822 (FIG. 8), magnitude portion 824 (FIG. 8) and aplurality of magnitude portions (not shown) may also be described by theillustration of FIG. 12.

Magnitude portion 822 includes a complex conjugate portion 1202 and amultiplier portion 1204. Each of the elements of magnitude portion 822are illustrated as individual devices, however, in some embodiments ofthe present invention at least two of complex conjugate portion 1202 andmultiplier portion 1204 may be combined as a unitary device.

Complex conjugate portion 1202 may receive a signal 1206 generatedexternal to magnitude portion 822. Multiplier portion 1204 may receivesignal 1206 generated external to magnitude portion 822, a signal 1208from complex conjugate portion 1202 and provide a signal 1210 fordelivery external to complex conjugate portion 1202.

Magnitude portion 822 may receive a signal generated from external tomagnitude portion 822, perform a complex conjugate operation for thereceived signal, perform a multiplication operate of the received signaland the complex conjugate calculation to generate a magnitudecalculation for the received signal. Furthermore, the magnitudecalculation may be provided for delivery external to magnitude portion822.

As an example, magnitude portion 822 may receive a value of (2+j3) inorder to determine the magnitude. Complex conjugate portion 1202 maycalculate the complex conjugate for (2+j3) denoted as (2−j3). Multiplierportion 1204 may then multiply (2+j3)*(2−j3) and generate a magnitudevalue of 13 for delivery external to magnitude portion 822.

FIG. 13 illustrates a detailed version of example signal parameterestimator 826 (FIG. 8), in accordance with an aspect of the presentinvention.

Signal parameter estimator 826 includes a processor portion 1302 and amemory portion 1304. Each of the elements of signal parameter estimator826 are illustrated as individual devices, however, in some embodimentsof the present invention at least two of processor portion 1302 andmemory portion 1304 may be combined as a unitary device.

Processor portion 1302 may receive a plurality of signals containingmagnitude information, with a sampling denoted as a signal 1308, asignal 1310 and a signal 1312, and receive a signal 1306 containinginformation for decoding. Processor portion 1302 may communicatebi-directionally with memory via a communication channel 1314.

Processor portion 1302 may receive the plurality of signals containingmagnitude information and store the magnitude information in memoryportion 1304. Processor may retrieve magnitude information from memoryportion 1304 for processing. Processor portion 1302 may performthreshold calculations and comparisons for the magnitude information inorder to determine the receipt and match for a unique word. Furthermore,processor portion 1302 may use the determination of a unique word matchfor determining synchronization information and phase information fordecoding information received via signal 1306 for deliver external tosignal parameter estimator 826 via a signal 1316.

Non-limiting examples of the processing functions performed by signalparameter estimator 826 include threshold calculations, thresholdcomparisons, time related calculations, frequency related calculations,interpolation calculations and decoding operations.

FIG. 14 illustrates an example matrix 1402 of magnitude information ascalculated by example parameter estimator 704 (FIGS. 7-8), in accordancewith an aspect of the present invention.

Matrix 1402 includes a plurality of row information with a samplingdenoted as a row 1404, a row 1406, a row 1408, a row 1401 and a row 1412and a plurality of column information with a sampling denoted as acolumn 1414, a column 1416, a column 1418, a column 1420, a column 1422,a column 1424 and a column 1426.

The rows of matrix 1402 may be organized by frequency offset asdetermined by a plurality of phase-shill coefficients with a samplingdenoted, referring to FIG. 10, as phase-shift coefficient 1008,phase-shift coefficient 1010 and phase-shift coefficient 1012. Thecolumns of matrix 1402 may be organized with respect to time with theinformation depicted in column 1414 as being received prior toinformation received in other columns and with the information depictedin column 1426 as being received after information received in othercolumns.

The magnitude information as depicted in matrix 1402 may indicate afrequency offset and moment of time for synchronization with an expectedunique word for a received signal. For example, the largest value ofmagnitude as depicted in matrix 1402 is the value of eight located atthe intersection of row 1406 and column 1422. For this example, the timeand frequency offset may be determined as being with respect to thefrequency offset of row 1406 and with respect to the timing of column1422.

Furthermore, the exact time and frequency for synchronization may notoccur at exactly the intersection of row 1406 and column 1422. A case ofinexact synchronization may be observed by significant, but lowermagnitude, values located adjacent to the largest magnitude value. Forexample, the next largest magnitude values of matrix 1402 are located inadjacent positions to the largest magnitude value of 8. The significantbut lesser magnitude values may be observed as a value of 7 located atthe intersection of row 1404 and column 1422 and by a value 6 located atthe intersection of row 1406 and column 1420. A more accuraterepresentation for the time and frequency for synchronization may bedetermined by performing an interpolation calculation between thelargest value of magnitude and lesser valued adjacent magnitude values.For example, the true frequency offset may be considered as between thefrequency offset as denoted by column 1422 and column 1420 and the truetime offset may be considered as between the time offset as denoted byrow 1404 and row 1406.

FIGS. 15A-B illustrate an exemplary method 1500 for operation of signalparameter estimator 826, in accordance with an aspect of the presentinvention.

Starting with FIG. 15A, in the example embodiment, method 1500 starts(S1502) and signal parameter estimator 826 may receive and store amatrix of information as depicted, by the exemplary embodiment asillustrated in FIG. 14 (S1504).

Returning to FIG. 13, processor portion 1302 may receive magnitudeinformation via a plurality of signals with a sampling denoted as signal1308, signal 1310 and signal 1312. Processor portion 1302 may then storereceived magnitude information in memory portion 1304 via communicationchannel 1314.

Matrix of magnitude information may be retrieved and examined byprocessor portion 1302 (S1506).

Processor portion 1302 may retrieve matrix of magnitude information frommemory portion 1304 via communication channel 1314 and examine theelements of the retrieved matrix for magnitude elements of the matrixexceeding a predetermined threshold.

For a determination of not finding a value of the matrix greater thanthe predetermined threshold, execution of method 1500 returns toreceiving and storing matrix information (S1504).

For a determination of finding a value of the matrix greater than thepredetermined threshold (S1508), a determination for the frequencyoffset and time offset is made (S1510) based upon the respective row andcolumn of the matrix for an element or elements exceeding thepredetermined threshold.

For example, returning to FIG. 14, the magnitude value of 8 located asthe cross section of row 1406 and column 1422, as depicted in exemplarymatrix 1402, may be considered as having the maximum value of all of theelements of the matrix and surpassing a threshold value of 5.Furthermore, the frequency offset may be determined approximately asbeing with respect to row 1406 and the time offset may be determinedapproximately as being with respect to column 1422.

After determining a maximum magnitude for a matrix of information, themagnitude of neighboring elements to the maximum magnitude for thematrix may be examined for significance in order to determine if a moreaccurate estimate for the time and frequency offset may be ascertained(S1512).

As illustrated in FIG. 15B, for a determination of significantneighboring elements of the maximum magnitude value (S1514), aninterpolated value for the time and/or frequency offset may becalculated (S1516).

For example, returning to FIG. 14, the magnitude value of 7 located atthe cross section of row 1404 and column 1422 may be considered greaterthan a threshold of 5. Furthermore, the magnitude value of 6 located atthe cross section of row 1406 and column 1420 may be considered greaterthan a threshold of 5. Based on this a more accurate approximation forthe frequency offset may be determined via interpolation as beinglocated between the frequency as indicated by row 1404 and row 1406.Furthermore, a more accurate approximation for the time offset may bedetermined via interpolation as being located between the time asindicated by column 1420 and column 1422. Any known method forinterpolation calculation may be used for determining more accurateapproximations for the time and frequency offset.

After determining a time and frequency offset, the received signal maybe processed for decoding the embedded symbols (S1518).

For example, returning to FIG. 2, consider frame 204. The starting timeof frame 204, as denoted by time 208, may be determined, as well as anyfrequency offset. Using the time and frequency information derived fromprocessing unique word 216, signal parameter estimator 826, asillustrated in FIG. 8, may determine the start time of payload 218, asdenoted by time 220. Furthermore, signal parameter estimator 826 maydetermine the starting time and frequency offset for each symbol ofpayload 218. Furthermore, having determined the starting time andfrequency offset for each symbol, signal parameter estimator 826 maydetermine the value of each symbol resident within payload 218.Furthermore, signal parameter estimator 826 may transmit decodeinformation external to communication receiver portion 700.

After decoding information embedded in a signal, it may be determinedwhether method 1500 continues execution (S1520).

For a determination of continuation of method 1500, execution of method1500 returns to receiving and storing matrix information (S1504) (FIG.15A).

For a determination of cessation of method 1500, method 1500 terminates(S1522) (FIG. 15B).

A data processor may receive a matrix of magnitude information, storeinformation, retrieve information, process information, examineinformation, determine a time and frequency offset, performinterpolation operations to determine a more accurate representation ofthe time and frequency offset and use time and frequency offset toperform processing and decoding of information embedded within areceived signal.

In accordance with an aspect of the present invention, a system andmethod has been described for receiving an encoded signal containingimpairments and for providing filtering, demodulation and processing forthe near optimal recovery of the encoded information embedded within thereceived signal.

The foregoing description of various preferred embodiments of theinvention have been presented for purposes of illustration anddescription. It is not intended to be exhaustive or to limit theinvention to the precise forms disclosed, and obviously manymodifications and variations are possible in light of the aboveteaching. The example embodiments, as described above, were chosen anddescribed in order to best explain the principles of the invention andits practical application to thereby enable others skilled in the art tobest utilize the invention in various embodiments and with variousmodifications as are suited to the particular use contemplated. It isintended that the scope of the invention be defined by the claimsappended hereto.

1. A system for use with a frequency band including a transmissionfrequency and a received frequency, the transmission frequency includinga transmission signal having a transmitted unique word therein, thereceived frequency including a received signal having a received uniqueword therein, the received unique word having been received at areceived time and at a received phase, said system comprising: a firstsub-correlator operable to perform a first correlation of only a firstportion of the received unique word with a corresponding first portionof the transmitted unique word over a plurality of instances of time andto output a first plurality of sub-correlation values; a secondsub-correlator operable to perform a second correlation of only a secondportion of the received unique word with a corresponding second portionof the transmitted unique word over the plurality of instances of timeand to output a second plurality of sub-correlation values; and adiscrete Fourier transform device operable to perform a discrete Fouriertransform over a plurality of frequencies within the frequency band onthe first plurality of sub-correlation values and to perform a discreteFourier transform over the plurality of frequencies within the frequencyband on the second plurality of sub-correlation values, wherein thefirst portion of the received unique word is different from the secondportion of the received unique word.
 2. The system of claim 1, whereinsaid discrete Fourier transform device is operable to output a matrix ofvalues.
 3. The system of claim 2, wherein said discrete Fouriertransform device is operable to output the matrix of values as a matrixof complex values.
 4. The system of claim 3, further comprising aprocessing portion operable to calculate a matrix of magnitude valuesbased on the matrix of complex values.
 5. The system of claim 4, whereinsaid processing portion is further operable to interpolate about thegreatest magnitude value within the matrix of magnitude values to obtaina maximum magnitude value.
 6. A method of using a frequency bandincluding a transmission frequency and a received frequency, thetransmission frequency including a transmission signal having atransmitted unique word therein, the received frequency including areceived signal having a received unique word therein, the receivedunique word having been received at a received time and at a receivedphase, said method comprising: performing, via a first sub-correlator, afirst correlation of only a first portion of the received unique wordwith a corresponding first portion of the transmitted unique word over aplurality of instances of time and to output a first plurality ofsub-correlation values; performing, via a second sub-correlator, asecond correlation of only a second portion of the received unique wordwith a corresponding second portion of the transmitted unique word overthe plurality of instances of time and to output a second plurality ofsub-correlation values; and performing, via a discrete Fourier transformdevice, a discrete Fourier transform over a plurality of frequencieswithin the frequency band on the first plurality of sub-correlationvalues and to perform a discrete Fourier transform over the plurality offrequencies within the frequency band on the second plurality ofsub-correlation values, wherein the first portion of the received uniqueword is different from the second portion of the received unique word.7. The method of claim 6, wherein said performing, via a discreteFourier transform device, a discrete Fourier transform comprisesoutputting a matrix of values.
 8. The method of claim 7, wherein saidoutputting a matrix of values comprises outputting the matrix of valuesas a matrix of complex values.
 9. The method of claim 8, furthercomprising calculating, via a processing portion, a matrix of magnitudevalues based on the matrix of complex values.
 10. The method of claim 9,further comprising interpolating, via the processing portion, about thegreatest magnitude value within the matrix of magnitude values to obtaina maximum magnitude value.
 11. A computer-readable media havingcomputer-readable instructions stored thereon, the computer-readableinstructions being capable of being read by a computer to be used with afrequency band including a transmission frequency and a receivedfrequency, the transmission frequency including a transmission signalhaving a transmitted unique word therein, the received frequencyincluding a received signal having a received unique word therein, thereceived unique word having been received at a received time and at areceived phase, the computer-readable instructions being capable ofinstructing the computer to perform the method comprising: performing,via a first sub-correlator, a first correlation of only a first portionof the received unique word with a corresponding first portion of thetransmitted unique word over a plurality of instances of time and tooutput a first plurality of sub-correlation values; performing, via asecond sub-correlator, a second correlation of only a second portion ofthe received unique word with a corresponding second portion of thetransmitted unique word over the plurality of instances of time and tooutput a second plurality of sub-correlation values; and performing, viaa discrete Fourier transform device, a discrete Fourier transform over aplurality of frequencies within the frequency band on the firstplurality of sub-correlation values and to perform a discrete Fouriertransform over the plurality of frequencies within the frequency band onthe second plurality of sub-correlation values, wherein the firstportion of the received unique word is different from the second portionof the received unique word.
 12. The computer-readable media of claim11, wherein the computer-readable instructions being capable ofinstructing the computer to perform a discrete Fourier transformcomprises computer-readable instructions being capable of instructingthe computer to output a matrix of values.
 13. The computer-readablemedia of claim 12, wherein the computer-readable instructions beingcapable of instructing the computer to output a matrix of valuescomprises computer-readable instructions being capable of instructingthe computer to output the matrix of values as a matrix of complexvalues.
 14. The computer-readable media of claim 13, wherein thecomputer-readable instructions being further capable of instructing thecomputer to perform calculating, via a processing portion, a matrix ofmagnitude values based on the matrix of complex values.
 15. Thecomputer-readable media of claim 14, wherein the computer-readableinstructions being further capable of instructing the computer toperform interpolating, via the processing portion, about the greatestmagnitude value within the matrix of magnitude values to obtain amaximum magnitude value.